Table Of ContentContents Contents
Differential Equations
in Engineering
Mathematical Engineering, Manufacturing,
and Management Sciences
Series Editor
Mangey Ram
Professor, Assistant Dean (International Affairs), Department of Mathematics,
Graphic Era University, Dehradun, India
The aim of this new book series is to publish the research studies and articles that bring up the
latest development and research applied to mathematics and its applications in the manufacturing
and management sciences areas. Mathematical tool and techniques are the strength of engineer-
ing sciences. They form the common foundation of all novel disciplines as engineering evolves
and develops. The series will include a comprehensive range of applied mathematics and its
application in engineering areas such as optimization techniques, mathematical modelling and
simulation, stochastic processes and systems engineering, safety-critical system performance,
system safety, system security, high assurance software architecture and design, mathematical
modelling in environmental safety sciences, finite element methods, differential equations, reli-
ability engineering, etc.
Partial Differential Equations: An Introduction
Nita H. Shah and Mrudul Y. Jani
Linear Transformation
Examples and Solutions
Nita H. Shah and Urmila B. Chaudhari
Matrix and Determinant
Fundamentals and Applications
Nita H. Shah and Foram A. Thakkar
Non-Linear Programming
A Basic Introduction
Nita H. Shah and Poonam Prakash Mishra
Applied Soft Computing and Embedded System Applications in Solar Energy
Rupendra Kumar Pachauri, J. K. Pandey, Abhishek Sharma, Om Prakash Nautiyal, Mange Ram
Differential Equations in Engineering
Research and Applications
Edited by Nupur Goyal, Piotr Kulczycki, and Mangey Ram
Sustainability in Industry 4.0
Challenges and Remedies
Edited by Shwetank Avikal, Amit Raj Singh, Mangey Ram
Applied Mathematical Modeling and Analysis in Renewable Energy
Edited by Manoj Sahni and Ritu Sahni
For more information about this series, please visit: https: // www . rout ledge . com/ Mathe matic al- E
nginee ring- Manuf actur ing-a nd- Ma nagem ent-S cienc es/ bo ok- se ries/ CRCME MMS
Differential Equations
in Engineering
Research and Applications
Edited by
Nupur Goyal, Piotr Kulczycki, and Mangey Ram
First edition published 2022
by CRC Press
6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742
and by CRC Press
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© 2022 Nupur Goyal, Piotr Kulczycki, and Mangey Ram
CRC Press is an imprint of Taylor & Francis Group, LLC
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Library of Congress Cataloging-in-Publication Data
Names: Goyal, Nupur, editor. | Kulczycki, Piotr, editor. | Ram, Mangey,
editor.
Title: Differential equations in engineering : research and applications /
edited by Nupur Goyal, Piotr Kulczycki, and Mangey Ram.
Description: First edition. | Boca Raton, FL : CRC Press, 2022. | Series:
Mathematical engineering, manufacturing, and management sciences |
Includes bibliographical references and index.
Identifiers: LCCN 2021011041 (print) | LCCN 2021011042 (ebook) | ISBN
9780367613129 (hbk) | ISBN 9780367613143 (pbk) | ISBN 9781003105145
(ebk)
Subjects: LCSH: Engineering mathematics. | Differential equations.
Classification: LCC TA347.D45 D45 2022 (print) | LCC TA347.D45 (ebook) |
DDC 620.001/51535--dc23
LC record available at https://lccn.loc.gov/2021011041
LC ebook record available at https://lccn.loc.gov/2021011042
ISBN: 978-0-367-61312-9 (hbk)
ISBN: 978-0-367-61314-3 (pbk)
ISBN: 978-1-003-10514-5 (ebk)
Typeset in Times
by Deanta Global Publishing Services, Chennai, India
Contents
Preface......................................................................................................................vii
Acknowledgments .....................................................................................................ix
Editors .......................................................................................................................xi
Contributors ...........................................................................................................xiii
Chapter 1 Element-Free Galerkin Method for Computational
Fracture Mechanics ..............................................................................1
Mohit Pant
Chapter 2 Evaporative Capillary Instability of Swirling Fluid Layer
with Mass Transfer .............................................................................37
Mukesh Kumar Awasthi, Rishi Asthana, and Ziya Uddin
Chapter 3 Control Instruments of Regularized Problems Based on
Mathematical Modeling of Structural Perturbations with
Applications at the Nodes of 25-Bar Truss Systems ..........................55
Koumbe Mbock, Etoua Remy Magloire, and Ayissi Raoul Domingo
Chapter 4 Numerical Simulation of Singularly Perturbed Differential
Equation with Large Delay Using Exponential B-Spline
Collocation Method ............................................................................77
Geeta Arora and Mandeep Kaur Vaid
Chapter 5 Application of Differential Equations to Instability of Nanofluids ......95
Jyoti Sharma
Chapter 6 Analysis of Prey–Predator Model ....................................................107
Purnima Pandit, Payal Singh, and Tanvi Patel
Chapter 7 Incremental Harmonic Balance Method for Multi-
Degree-of-Freedom System with Time-Delays ................................125
R.K. Mitra
v
vi Contents
Chapter 8 Solution to the Dirac Equation .........................................................145
S.K. Pandey
Chapter 9 Periodic Solution of a Nonlinear Economic Cycle Model
with a Generic Investment Function ................................................155
Jun Zhao
Chapter 10 Response Evolution of a Marine Riser in Random Sea Waves ........171
Haitao Zhu, Guoqian Geng, Yang Yu, and Lixin Xu
Chapter 11 Solution of System of PDE Governed in Natural Convective
Flow in a Rectangular Porous Cavity ...............................................187
P. Alam and S. Kapoor
Index ......................................................................................................................207
Preface
Creating mathematical models of real objects constitutes a fundamental aspect of
modern science and various practical applications. The classical tool, especially in
the mechanical and electrical engineering disciplines, is provided here by the theory
of differential equations. The resulting formal apparatus is the basis of many practi-
cal disciplines, e.g., optimal and robust control, and theory of chaos or dynamical
systems. Other fields in which differential equations are widely used include broad
areas of mathematics such as linear algebra, numerical methods, and many others. It
is worth emphasizing the close, mutually inspiring connections between differential
equations and physics. After mathematical statistics, differential equations are cur-
rently the most important discipline in applied mathematics, especially in engineer-
ing and economics, as well as recently in the natural sciences. They are of value to
students and graduates in the above disciplines in recognizing and understanding the
laws that govern the surrounding world.
This book touches upon a number of specific aspects of the theory and practice
of differential equations. Such a breadth of subject matter relates to a large degree to
the fact that the fundamental problems of differential equations have already been
sufficiently widely described in the subject literature. The scope of this book con-
cerns both linear issues, which often have analytical solutions, and nonlinear ones,
frequently supported by numerical methods. The following topics are covered in this
monograph:
• Element-free Galerkin methods in computational fracture mechanics.
• Evaporative capillary instability of swirling fluid layer with mass transfer.
• Control instruments of regularized problems based on mathematical mod-
eling of structural perturbations with applications at the nodes of 25 bar
truss systems.
• Numerical simulation of singularly perturbed differential equations with
large delays, using exponential B-spline collocation method.
• Application of differential equations to understanding the instability of
binary nanofluids.
• Mathematical modeling and analysis of prey-predator models.
• The incremental harmonic balance method for multiple degrees-of-freedom
systems with time delays.
• Solution to the Dirac equation.
• Periodic solution of a nonlinear economic cycle model with a generic
investment function.
• Response evolution of a marine riser in random sea waves.
• Solution of a system of partial differential equations governed by natural
convective flow in a porous cavity.
vii
viii Preface
At the end of each chapter there is a list of subject literature, facilitating further
exploration of the individual topics.
We wish the readers a successful study of the material presented, leading to new
inspiration, a deepening understanding of the described concepts, and also fruitful
applications to the contemporary challenges of science and practice.
Dr. Nupur Goyal
Prof. (D.Sc.) Piotr Kulczycki
Prof. (Dr.) Mangey Ram
Acknowledgments
We express our sincere thanks to the team at CRC Press, Taylor & Francis Group for
giving us this opportunity and for support during this project. Particular gratitude
is due to Ms. Cindy Renee Carelli, Executive Editor, CRC Press, Taylor & Francis
Group, for the excellent help provided by her to us in the approval for this book.
We would also like to acknowledge the help from Ms. Erin Harris, Senior Editorial
Assistant, CRC Press, Taylor & Francis Group.
Nupur Goyal
Piotr Kulczycki
Mangey Ram
ix
